int cfg_expand_clique(CFG *G, int c_len, int c_ind[])
{ int nv = G->nv;
int d_len, *d_ind, *d_pos, len, *ind;
int k, v;
xassert(0 <= c_len && c_len <= nv);
/* allocate working arrays */
d_ind = talloc(1+nv, int);
d_pos = talloc(1+nv, int);
ind = talloc(1+nv, int);
/* initialize C := 0, D := V */
d_len = nv;
for (k = 1; k <= nv; k++)
d_ind[k] = d_pos[k] = k;
/* expand C by vertices of specified initial clique C0 */
for (k = 1; k <= c_len; k++)
{ /* v in C0 */
v = c_ind[k];
xassert(1 <= v && v <= nv);
/* since C0 is clique, v should be in D */
xassert(d_pos[v] != 0);
/* W := set of vertices adjacent to v */
len = cfg_get_adjacent(G, v, ind);
/* D := D inter W */
d_len = intersection(d_len, d_ind, d_pos, len, ind);
/* since v not in W, now v should be not in D */
xassert(d_pos[v] == 0);
}
/* expand C by some other vertices until D is empty */
while (d_len > 0)
{ /* v in D */
v = d_ind[1];
xassert(1 <= v && v <= nv);
/* note that v is adjacent to all vertices in C (by design),
* so add v to C */
c_ind[++c_len] = v;
/* W := set of vertices adjacent to v */
len = cfg_get_adjacent(G, v, ind);
/* D := D inter W */
d_len = intersection(d_len, d_ind, d_pos, len, ind);
/* since v not in W, now v should be not in D */
xassert(d_pos[v] == 0);
}
/* free working arrays */
tfree(d_ind);
tfree(d_pos);
tfree(ind);
/* bring maximal clique to calling routine */
return c_len;
}
static int sub_adjacent(struct csa *csa, int i, int adj[])
{ /* retrieve vertices of induced subgraph adjacent to specified
* vertex */
CFG *G = csa->G;
int nv = G->nv;
int *ind = csa->ind;
int nn = csa->nn;
int *vtoi = csa->vtoi;
int *itov = csa->itov;
int j, k, v, w, len, len1;
/* determine original vertex v corresponding to vertex i */
xassert(1 <= i && i <= nn);
v = itov[i];
/* retrieve vertices adjacent to vertex v in original graph */
len1 = cfg_get_adjacent(G, v, ind);
/* keep only adjacent vertices which are in induced subgraph and
* change their numbers appropriately */
len = 0;
for (k = 1; k <= len1; k++)
{ /* there exists edge (v, w) in original graph */
w = ind[k];
xassert(1 <= w && w <= nv && w != v);
j = vtoi[w];
if (j != 0)
{ /* vertex w is vertex j in induced subgraph */
xassert(1 <= j && j <= nn && j != i);
adj[++len] = j;
}
}
return len;
}
void cfg_check_clique(CFG *G, int c_len, const int c_ind[])
{ int nv = G->nv;
int k, kk, v, w, len, *ind;
char *flag;
ind = talloc(1+nv, int);
flag = talloc(1+nv, char);
memset(&flag[1], 0, nv);
/* walk thru clique vertices */
xassert(c_len >= 0);
for (k = 1; k <= c_len; k++)
{ /* get clique vertex v */
v = c_ind[k];
xassert(1 <= v && v <= nv);
/* get vertices adjacent to vertex v */
len = cfg_get_adjacent(G, v, ind);
for (kk = 1; kk <= len; kk++)
{ w = ind[kk];
xassert(1 <= w && w <= nv);
xassert(w != v);
flag[w] = 1;
}
/* check that all clique vertices other than v are adjacent
to v */
for (kk = 1; kk <= c_len; kk++)
{ w = c_ind[kk];
xassert(1 <= w && w <= nv);
if (w != v)
xassert(flag[w]);
}
/* reset vertex flags */
for (kk = 1; kk <= len; kk++)
flag[ind[kk]] = 0;
}
tfree(ind);
tfree(flag);
return;
}
static void build_subgraph(struct csa *csa)
{ /* build induced subgraph */
glp_prob *P = csa->P;
int n = P->n;
CFG *G = csa->G;
int *ind = csa->ind;
int *pos = G->pos;
int *neg = G->neg;
int nv = G->nv;
int *ref = G->ref;
int *vtoi = csa->vtoi;
int *itov = csa->itov;
double *wgt = csa->wgt;
int j, k, v, w, nn, len;
double z, sum;
/* initially induced subgraph is empty */
nn = 0;
/* walk thru vertices of original conflict graph */
for (v = 1; v <= nv; v++)
{ /* determine value of binary variable z[j] that corresponds to
* vertex v */
j = ref[v];
xassert(1 <= j && j <= n);
if (pos[j] == v)
{ /* z[j] = x[j], where x[j] is original variable */
z = P->col[j]->prim;
}
else if (neg[j] == v)
{ /* z[j] = 1 - x[j], where x[j] is original variable */
z = 1.0 - P->col[j]->prim;
}
else
xassert(v != v);
/* if z[j] is close to zero, do not include v in the induced
* subgraph */
if (z < 0.001)
{ vtoi[v] = 0;
continue;
}
/* calculate cumulative weight of vertex v */
sum = z;
/* walk thru all vertices adjacent to v */
len = cfg_get_adjacent(G, v, ind);
for (k = 1; k <= len; k++)
{ /* there is an edge (v,w) in the conflict graph */
w = ind[k];
xassert(w != v);
/* add value of z[j] that corresponds to vertex w */
j = ref[w];
xassert(1 <= j && j <= n);
if (pos[j] == w)
sum += P->col[j]->prim;
else if (neg[j] == w)
sum += 1.0 - P->col[j]->prim;
else
xassert(w != w);
}
/* cumulative weight of vertex v is an upper bound of weight
* of any clique containing v; so if it not greater than 1, do
* not include v in the induced subgraph */
if (sum < 1.010)
{ vtoi[v] = 0;
continue;
}
/* include vertex v in the induced subgraph */
nn++;
vtoi[v] = nn;
itov[nn] = v;
wgt[nn] = z;
}
/* induced subgraph has been built */
csa->nn = nn;
return;
}
